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Animation of the missing square puzzle, showing the two arrangements of the pieces and the "missing" square Both "total triangles" are in a perfect 13×5 grid; and both the "component triangles", the blue in a 5×2 grid and the red in an 8×3 grid.
A similar problem asks if a wazir starting at a corner square of an ordinary chessboard can visit every square exactly once, and finish at the opposite corner square. The wazir is a fairy chess piece that can move only one square vertically or horizontally (not diagonally). Using similar reasoning to the mutilated chessboard problem's classic ...
The multi-tile metric counts subsequent moves of the empty tile in the same direction as one. [6] The number of possible positions of the 24 puzzle is 25! / 2 ≈ 7.76 × 10 24, which is too many to calculate God's number feasibly using brute-force methods. In 2011, lower bounds of 152 single-tile moves or 41 multi-tile moves had been ...
This is a list of puzzles that cannot be solved. An impossible puzzle is a puzzle that cannot be resolved, either due to lack of sufficient information, or any number of logical impossibilities. 15 Puzzle – Slide fifteen numbered tiles into numerical order. It is impossible to solve in half of the starting positions.
This is equal to the square of the number of grains on the first half of the board, plus itself. The first square of the second half alone contains one more grain than the entire first half. On the 64th square of the chessboard alone, there would be 2 63 = 9,223,372,036,854,775,808 grains, more than two billion times as many as on the first ...
An independence problem (or unguard [2]) is a problem in which, given a certain type of chess piece (queen, rook, bishop, knight or king), one must find the maximum number that can be placed on a chessboard so that none of the pieces attack each other. It is also required that an actual arrangement for this maximum number of pieces be found.
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In this puzzle, the numbers are a form of discrete tomography that measures how many unbroken lines of filled-in squares there are in any given row or column. For example, a clue of "4 8 3" would mean there are sets of four, eight, and three filled squares, in that order, with at least one blank square between successive sets.